I don't really understand some of this notation. I was wondering if someone could help me determine which of the following are subspaces and why they fail to be subspaces (if they are not).

Let R[X] denote the vector space (over R) of polynomials with real coefficients. Which of the following are subspaces of R[X]?

a) The set of odd polynomials.

b) The set of polynomials of odd degree (We include the polynomial 0).

c) {p(X) in R[X]: p(i*sqrt(3))=0}.

d) {p(X) in R[X]: p(0)= i*sqrt(3)}.

e) The set {(X^2+3)(p(X)): p(X) in R[X]}.

f) The set {(X-i*sqrt(3))p(X): p(X) in R[X]}.

g) The set of polynomials with rational coefficients.

h) {p(X) in R[X]: p(i*sqrt(3)) is real}.

Thank you so much for any help.